He’s talking about when people who would otherwise have worn their hat during all of davening go on to get married and switch to a tallis, they either only cover their head with it for minimal amounts of davening, or never at all.
Not all if davening is equal – when wearing a hat, it’s easier to keep it on. It’s not a downgrade b’shita, the hat wasn’t worn the entire davening other than out of convenience.
I don’t believe not covering during Shacharis Shemoneh Esreh is common for ir those who wear a hat for other tefillos.